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Suppose g(x) is a real valued differenti...

Suppose `g(x)` is a real valued differentiable function satisfying `g'(x) + 2g(x) gt 1.` Then show that `e^(2x)(g(x)-1/2)` is an increasing function.

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To show that \( e^{2x}(g(x) - \frac{1}{2}) \) is an increasing function, we will follow these steps: ### Step 1: Define the function Let \[ f(x) = e^{2x} \left( g(x) - \frac{1}{2} \right). \] ...
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